**3. Chirality in crystals**

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interactions, and different crystal structures. [30, 31]

analysis are beyond the scope of this chapter.

which will be discussed in detail.

A chiral structure is non-superimposable on its mirror image. Pasteur reported in 1984 the concept of the molecular Chirality based on the distinction between the configurational isomers of molecules. Configurational isomers are compounds with the same molecular formula and same groups but different configurations. Enantiomers are pairs of configurational isomers that are mirror images of each other but are non-superimposable. Diastereomers are pairs of compounds that contain more than one chiral center, not all of which are superimposable. An equimolar mixture of opposite enantiomers is called racemic mixture or a racemate. Enantiomers when exposed to polarized light behave differently and have different catalyzing properties in a chiral medium. On the other hand, the racemic mixtures have completely different properties than enantiomers. The difference in the properties between the enantiomers and racemic mixtures arise due to different molecular

In an enantiomer, the molecular interactions are homochiral, which are the interactions between the assemblies of molecules with same Chirality. In a racemic compound the interactions are heterochiral, where the interactions are between opposite chiral molecules. The difference between the homochiral and heterochiral interactions leads to different physical properties. Particularly in a racemic compound, because the unit cell consists of enantiomeric molecules with opposite Chirality, the properties are completely different from enantiomers. Racemic compounds are the most common compounds that occur in nature. Such racemic compounds can exist in different forms based on the intermolecular interactions in their crystals. Analysis of the crystal structures facilitates enormously our understanding of the factors that determine the various physical and chemical properties, such as the thermodynamic stability of different types of racemates. [32] The details of such

Due to the presence of various chiral compounds, it is critical to have the right nomenclature for the differentiation. The internationally accepted nomenclature for chiral molecules uses the Cahn-Ingold-Prelog (CIP) rules for sp3 carbons. The four substituents are sorted by increasing mass of the first atom attached to the asymmetric center. If two atoms are identical, the next heaviest atom one bond further away is considered and so on. For example, in the case of 2-butanol with the order OH ethyl methyl rotating clockwise will be a R-enantiomer and the mirror image of that will be a S-enantiomer. These rules allow us for the absolute configuration of any chiral compounds. Another accepted form for nomenclature is Dextro (D-) and Levo (L-), based on the optical rotation of the compound. Setting glycine apart since it is nonchiral, it must be noted that all amino acids found in proteins are L-amino acids and also have the S-configuration at the exception of cysteine whose -CH2-SH substituent precedes the carboxylate -COOH in mass making L-cysteine the R-enantiomer. It is interesting to note that the electrodeposited chiral films also follow the CIP rules. It was shown that the CuO films grown from both R versions of tartaric acid and malic acid resulted in (1-1-1) orientation on Cu(111), while the S version of each resulted in a (-111) mirror image. [33] However, there are exceptions for films grown from amino acids

**2. Chirality** 

The Chirality of a crystal depends on the symmetry operations present in the structure. Proper symmetry operations are those that do not change the handedness of an object. These operations include rotation axes, translations, and screw axes. If an object can be rotated about an axis and repeats itself after being rotated through either 360, 180, 120, 90 or 60o is said to have an axis of 1-fold, 2-fold, 3- fold, 4-fold, or 6-fold rotational symmetry. Although objects themselves may appear to have 5-fold, 7-fold, 8-fold or higher-fold rotation axes, these are not possible in crystals. The reason is that the external shape of a crystal is based on a geometric arrangement of atoms. In a translation operation, the object is translated up or down along an axes. Where as a screw axis also referred to as twist axis of an object are the axes that are simultaneously the axis of rotation and the axis along which a translation occurs. These symmetry operations do not change the original object because they are just movements of the same object. If only these operations are present, then the structure is chiral. However, improper symmetry operations such as rotoinversion operations or glide reflection produce the opposite "hand" of the object. [34] A rotoinversion operation is a combination of rotation and inversion where as the glide reflection is a combination of reflection and translation operation along a line. Any structure with one of these symmetery operators will produce an achiral structure.

The symmetry of the system determines what planes of a material are chiral. In the case of copper(II) oxide CuO (focus material in this chapter), the lattice parameters are a = 0.4685 nm, b = 0.3430 nm, c = 0.5139 nm, α=ϒ= 90o, and β= 99.08o. The structure is centrosymmetric (i.e. it has an inversion center, i); therefore, the bulk crystal structure of CuO is achiral. However, crystallographic orientations/planes may be chiral. A monoclinic system has three axes of unequal length and an angle normally greater than 90o between two axes. In this arrangement, the b'axis is unique. The c and a axes do not intersect each other at right angles, but they are perpendicular to the b-axis. Based on the space group, a glide plane has a mirror or glide plane perpendicular to it. Therefore, achiral planes of CuO are planes that are parallel to the b-axis, planes k=0. Thus, planes such as (101), (001), and (102) are achiral. Chiral CuO planes lack glide plane symmetry; chiral planes are those with k ≠ 0, such as (111), (110), (022), and (020). For a chiral plane (hkl), its enantiomer is (-h-k-l).

Table 1 lists the symmetry of specific planes depending on the point group. [35] Screw axes are replaced by the highest possible rotation, and glides are replaced by mirrors. Planes that lack mirror symmetry (m) are chiral. For example, whereas all planes of triclinic structure are chiral, all planes of orthorhombic structure are achiral except where h≠k≠l≠0, the space group of CuO is C2/c; its point group is 2/m. According to table 1, chiral planes are {010}, {0kl}, {hk0}, and {hkl}, whereas achiral planes are {100}, {001}, and {h01}. From these select planes, a trend is visible; achiral planes are those that k=0. This trend is t**r**ue for all monoclinic structures.

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**Table 1.** Symmetry of the planes of a point group. Orientations that lack mirror symmetry (i.e. having rotational symmetry) are chiral. The chiral orientations are highlighted in yellow.

Other methods to determine whether a surface is chiral or achiral are stereographic projections and interface models. Like a point group, stereographic projections is a twodimensional plot that shows the angular relationships of the crystal's planes and directions based on its crystallographic symmetry. Simply, a stereographic projection is a way to represent a three dimensional crystal on a two dimensional page. If two orientations have a stereographic projections that are superimpossible mirror images, then the orientations are achiral. If the two orientations produce stereographic projections that are nonsuperimposable mirror images, then the orientations are chiral.

Calculated stereographic projections are shown in figure 1 for the achiral planes (001) and (00-1) of CuO and in figure 2 for the chiral planes (111) and (-1-1-1) of CuO. In figure 1 A and 1B, the stereographic projections of the (001) and (00-1) planes are superimposable mirror images of each other. In addition, each projection has mirror symmetry. This mirror symmetry in the stereographic projection indicates that there is an improper symmetry operator perpendicular to this surface, resulting in planes that are achiral. In figure 2A and 2B, although the stereographic projections of the (111) and (-1-1-1) planes are mirror images of each other, they are not superimposable. Also, neither projection has mirror symmetry. The absence of mirror symmetry in the stereographic projection indicates that only proper symmetry operators are perpendicular to this surface. The presence of only symmetry operators indicates that these planes are chiral.

Thus based on the structure and orientation of the thin films, one can determine whether or not the film is chiral.
